Exactly what part of the circuit do you not understand? LDR is part of a voltage divider that will keep the base of Q1 at a point where Q1 is turned OFF when light is on the LDR. Can you take it from there?

RV1 sets the decision point. The LED should be off under normal lighting. If LDR1 is a CdS cell, it has less resistance in light. When dark happens, the resistance goes up. The resulting voltage goes to Q1 which amplifies current. That goes to Q2 which amplifies current. The LED becomes on.